Among the various approaches put forward to design ML potentials
[1]}, [2]}, the choice was made to set up a
high-dimensional neural network built in a similar way to the one
proposed by Behler and Parrinello [3]} and Zhang
et al. [4]}. This approach
has been proven successful for pure silicon [5]} as
well as water [6]} to model reliably both their
properties in the liquid and solid states. As a detailed description
can be found for instance in the tutorial review by Behler
[7]} among others, the focus is mainly made on the
specificity of our scheme. The main part consists in a supervised
learning task from a relevant sample of atomic configurations with
known energy generated by AIMD in various crystalline and liquids
structures in the desired temperature and pressure domain. In the
corresponding portion of Potential Energy Landscape (PEL), each
configurational energy is considered as a sum of individual atomic
energies determined from their local atomic environment within a
cut-off radius \(r_S\)  often extending beyond the first-neighbor
atomic shell, and taken here to be \(6.4\)  Å for Al. This
decomposition allows us to train \(N\)  Neural Networks (NN), each of
them being assigned to an individual local atomic environment. The
NN are then combined to recover the energy of the whole configuration
of \(N\)  atoms.
